两个矩阵的所有列组合的按分量乘积

Question

As the title says I want to calculate the component-wise product of all column combinations of two matrices. I already found a solution using numpy.einsum and numpy.hstack . I wonder if there is a solution without hstack .

Let a = [a_1, a_2, ..., a_n] be a dxn matrix and b = [b_1, b_2, ..., b_m] a dxm matrix. I want to calculate

[a_1b_1, a_1b_2, ..., a_nb_{n-1}, a_nb_n] ,

where a_kb_l is the component wise product, ie a_kb_l = [a_{1,k}*b{1,l}, ..., a_{d,k}*b{d,l}].T .

My solution is the following. np.hstack(np.einsum('...j,...l -> j...l', a, b))

Can I go without the h_stack ?

Answer 1

The following improvement replaces the hstack with a call of reshape . This releases quite a bit memory pressure when d is high.

np.einsum('...j,...l -> ...jl', a, b).reshape(d, -1)